Polarization independent grating

ABSTRACT

A grating has a high diffraction efficiency into the minus first diffracted order in transmission, for both TE and TM polarizations. The incident angle may optionally be chosen so that the minus first diffracted order in reflection would be retroreflected back to the incident beam. The grating may be formed from various materials and/or layers, where the thicknesses of the individual layers may be determined by an optimization or simulation process. In one aspect, the grating may have four or more layers, formed with three or more materials. In another aspect, the grating may have a longitudinal refractive index profile that contains at least two local extrema, such as a maximum and/or minimum. Such a grating may be formed from three or more materials, two materials, or a single material that has a continuously varying refractive index. Any or all of the materials may have a continuously varying refractive index profile, as well. In another aspect, the grating may include a material that has a continuously varying refractive index profile.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. application Ser. No.11/414,783 filed Apr. 28, 2006, now abandoned which is incorporatedherein by reference thereto in its entirety, as though fully set forthherein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed to gratings, and more particularly topolarization-independent transmission gratings.

2. Description of the Related Art

The dispersive effects of a diffraction grating are useful forseparating and/or combining optical beams as a function of wavelength.For instance, in the field of telecommunications, where differentchannels are transmitted over a single optical fiber, the channels aretypically spaced apart in wavelength, and a diffraction grating is oftenused as a dispersive element in a multiplexer and/or demultiplexer thatsplits out and/or adds in a particular channel.

The polarization state of a beam that passes through a multiplexerand/or demultiplexer may be the source of illumination loss fluctuationscaused by polarization fluctuations, commonly referred to as“polarization dependent loss”. This polarization dependent loss iscommonly expressed in decibels (dB), and represents the differencebetween the minimum and maximum transmitted powers through themultiplexer and/or demultiplexer, as the incident polarization is variedover all polarization states.

In many cases, a diffraction grating is a significant source ofpolarization dependent loss in a multiplexer and/or demultiplexer.Typically, the polarization loss can be traced back to a difference indiffraction efficiency between TE and TM polarized light, for aparticular diffracted order. For a transmission grating, in which thesignal passes through the minus first diffracted order in transmission,it is highly desirable to minimize the difference between the TEdiffraction efficiency and the TM diffraction efficiency for the minusfirst diffracted order in transmission. By reducing the differencebetween TE and TM polarizations in the grating, the polarizationdependent loss in the multiplexer and/or demultiplexer may also bereduced. In addition, it is generally desirable to maximize both the TEand TM diffraction efficiencies, which may also reduce the overall lossof the multiplexer and/or demultiplexer.

BRIEF SUMMARY OF THE INVENTION

An embodiment is an optical apparatus comprising an essentiallytransparent substrate; and a grating disposed adjacent the substrate andcomprising at least four grating layers of at least three essentiallytransparent and respectively different materials. The grating has aminus first order diffraction efficiency in transmission of greater than90% for both TE and TM polarizations.

Another embodiment is an optical apparatus, comprising an essentiallytransparent substrate; and a grating disposed adjacent the substrate,the grating having a longitudinal refractive index profile comprising atleast two local extrema. The grating has a minus first order diffractionefficiency in transmission of greater than 90% for both TE and TMpolarizations.

Another embodiment is an optical apparatus, comprising an essentiallytransparent substrate; and a grating disposed adjacent the substrate andhaving a material composition with a continuously varying longitudinalrefractive index profile. The grating has a minus first orderdiffraction efficiency in transmission of greater than 90% for both TEand TM polarizations.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a schematic drawing of a generic diffraction grating, anincident beam, TE and TM polarizations, and the orientations of variousdiffracted beams.

FIG. 2 is a schematic drawing of a grating, an incident beam, TE and TMpolarizations, and the orientations of the diffracted beams.

FIG. 3 is a schematic drawing of a grating, an incident beam, and adiffracted beam showing dispersion.

FIG. 4 is a schematic drawing of a grating having four layers and threematerials.

FIG. 5 is a schematic drawing of a grating having six layers and threematerials.

FIG. 6 is a plot of longitudinal refractive index profile of a gratinghaving four layers and two materials.

FIG. 7 is a plot of longitudinal refractive index profile of a gratinghaving four layers and two materials.

FIG. 8 is a plot of longitudinal refractive index profile of a gratinghaving four layers and three materials.

FIG. 9 is a plot of longitudinal refractive index profile of a gratinghaving four layers and three materials.

FIG. 10 is a plot of longitudinal refractive index profile of a gratinghaving a material with a continuously varying refractive index.

FIG. 11 is a plot of longitudinal refractive index profile of a gratinghaving a material with a continuously varying refractive index.

FIG. 12 is a plot of longitudinal refractive index profile of a gratinghaving a material with a continuously varying refractive index.

FIG. 13 is a plot of longitudinal refractive index profile of a gratinghaving a material with a continuously varying refractive index.

FIG. 14 is a plot of longitudinal refractive index profile of a gratinghaving a material with a continuously varying refractive index.

FIG. 15 is a plot of calculated minus first order diffractionefficiencies for TE and TM polarizations, as a function of wavelength,for a constant incident angle of 47 degrees, for an exemplary, six-layergrating.

FIG. 16 is a plot of polarization dependent loss, as a function ofwavelength, for a constant incident angle of 47 degrees, for theexemplary, six-layer grating of FIG. 15.

FIG. 17 is a plot of calculated minus first order diffractionefficiencies for TE and TM polarizations, as a function of incidentangle, for a constant wavelength of 1550 nm, for the exemplary,six-layer grating of FIG. 15.

DETAILED DESCRIPTION OF THE INVENTION

Because diffraction gratings will be discussed in detail below, it isinstructive to provide an example of a generic grating and itsassociated quantities.

FIG. 1 shows a generic diffraction grating 11. An incident beam 12strikes the diffraction grating 11 and produces various reflected andtransmitted orders. For the numerical examples provided herein, it isassumed that the plane of incidence is perpendicular to the periodicfeatures; this is not a requirement in general and should not beconsidered a limitation.

The locations of the diffracted orders are given by the well-knowngrating equation:mλ=d(sin θ_(out)−sin θ_(in)),

where m is an integer denoting the mth spectral diffracted order, λ isthe wavelength of the incident beam, d is the center-to-center spacingof the periodic features of the grating (commonly called the gratingpitch or grating period), θ_(in) is the angle of incidence of theincident beam (formed between the incident ray vector and a surfacenormal), and θ_(out) is the angle of exitance of the mth diffractedorder. The sign convention for the angles is chosen so that the negativediffracted orders are diverted toward the incident beam, and thepositive diffracted orders are diverted away from the incident beam, asshown in FIG. 1.

It is possible, although not necessary, that one of the diffractedorders may be reflected along the same direction as the incident beam12. For example, In FIG. 1, the minus third order is reflected along thesame path as the incident beam 12. A common condition is that the minusfirst reflected order returns along the same path as the incident beam12; this condition and it occurs for an incident angle θ_(in)=sin⁻¹(λ/2d), for suitable values of wavelength λ and grating period d. Thisrelationship may be rewritten as d=λ/(2 sin θ_(in)), which gives a valueof the required grating period d in terms of a wavelength λ and adesired incident angle θ_(in). For incident angles in the range of about40 degrees to 55 degrees, the required grating period d may be in therange of about 0.6 to about 0.8 times the wavelength λ, if the gratingis to be used where the minus first order in reflection isretroreflected to the incident beam.

FIG. 1 shows the location of all the diffracted orders for particularvalues of wavelength, grating period and incident angle. However, FIG. 1does not show the relative power values contained in each order. Thepower values are typically expressed as the ratio of the power containedin a particular diffracted order, divided by the incident power; thisratio is known as the diffraction efficiency. In general, eachdiffracted order has its own diffraction efficiency.

For many applications, the grating may be designed to maximize thediffraction efficiency of a particular order, such as the minus firsttransmitted order. Accordingly, the diffraction efficiency of the minusfirst transmitted order may be close to 100%, while the diffractionefficiencies of all the other orders may be close to 0%. In general, thediffraction efficiencies of the various orders are determined in part bythe grating materials and the shape of the grating features, which mayinclude the grating depth, duty cycle and form.

The polarization state of the incident beam 12 is usually described interms of two orthogonal components. For one component, the electricfield vector is transverse to the plane of incidence; this component istypically denoted as “TE” polarization, and may alternatively be knownas “s-polarization”. For the other component, the magnetic field vectoris transverse to the plane of incidence; this component is typicallydenoted as “TM” polarization, and may alternatively be known as“p-polarization”. In FIG. 1, the plane of incidence is the plane of thepage, and the corresponding electric field vectors are shown for TE andTM polarizations. In general, the polarization state may be fullycharacterized by the ratio of TE to TM polarization components, and thephase between the TE and TM polarization components.

For many gratings, the diffraction efficiency of a particular order maybe different for TE and TM polarizations. In general, it is difficult todesign a grating that has essentially equal TE and TM diffractionefficiencies for a particular order, and special care must be taken whenselecting the materials and the shape for such a grating. In addition,if the TE and TM diffraction efficiencies are to be not only essentiallyequal, but also close to 100%, the design task becomes even moredifficult.

FIG. 2 shows an example of a transmission grating 21 fortelecommunications, which can be used as a dispersive element in amultiplexer and/or demultiplexer. An incident beam 22 strikes thegrating 21 at incident angle θ_(in). The minus first reflected order isretroreflected back to the incident beam, although this is not arequirement and should not be construed as a limitation. Two diffractedorders that satisfy the grating equation are the zeroth and minus firstorders, which are drawn and labeled in FIG. 2.

For this particular grating 21, it is desirable to have the diffractionefficiency of the minus first transmitted order 23 as large as possible,so that essentially all the power in the incident beam 22 is directedinto the minus first transmitted order 23, with a minimal amount ofpower being directed into the transmitted zeroth order, the reflectedzeroth order, and the reflected minus first order. These other threeorders are drawn as dotted lines, indicating that they exist, but theypreferably contain a minimal amount of optical power in them. Inaddition, the diffraction efficiency of the minus first transmittedorder may be maximized for both TE and TM polarizations, which are alsodrawn in FIG. 2.

FIG. 3 shows the diffraction grating 21 of FIG. 2 with amulti-wavelength incident beam 32. Although there are three wavelengthsshown in FIG. 3, denoted as λ₁, λ₂ and λ₃, there may be any number ofwavelengths present in the incident beam 32. The incident beam 32 mayhave a continuous spectrum, a discrete spectrum, or a combination ofboth. After transmission through the grating 21, the wavelengthcomponents are diffracted at slightly different angles, as shownschematically by the minus first order diffracted beams 33. Thediffraction angles are found by applying the grating equation for eachwavelength component.

As an example, consider a grating for use in the so-called “C-band” usedin the telecommunications field, which has a central wavelength of about1550 nm. For incident angles of about 45 degrees to 50 degrees, thegrating period may be about 1.0 to 1.1 microns so that the minus firstorder is retroreflected back to the incident beam. As a specificexample, for an incident angle of 48.5 degrees and a grating period ofabout 1.035 microns, the full C-band, spanned by a wavelength range of1550 nm±25 nm, has an angle of exitance of about 48.5 degrees ± about2.1 degrees. For this specific example, the wavelength λ₁, is 1525 nm,the wavelength λ₂ is 1550 nm and the wavelength λ₃ is 1575 nm. Note thatthe longer wavelength λ₃ diffracts at a larger angle than the shorterwavelength λ₁, although FIG. 3 is not necessarily drawn to scale.

It is desirable that the diffraction efficiency remain essentially thesame for the entire wavelength range over which the grating is to beused, for both TE and TM polarizations. For the numerical example above,this means that the diffraction efficiency of the minus firsttransmitted order should be roughly constant between 1525 nm and 1575nm, for both TE and TM polarizations. The wavelength range may bedefined in terms of a center wavelength, such as 1550 nm, and afull-width, such as 40 nm, 50 nm (as for the above example), 100 nm and150 nm. The full-widths may equivalently be expressed as a percentage ofthe center wavelength, such as 2.6%, 3.2%, 6.5% and 9.7%. Other suitablecenter wavelengths and full-widths may also be used.

Furthermore, in addition to all the design requirements for the gratingslisted above, the grating should have adequate tolerances on itsincident angle, so that its diffraction efficiencies do notsignificantly vary over a range of incident angles. Suitable rangesinclude 6 degrees (meaning that the incident angle may vary by −3 to +3degrees), 10 degrees, and 20 degrees, although other suitable ranges maybe used. In addition, the grating should have adequate manufacturingtolerances so that reasonable variation in the grating parameters do notunduly affect the diffraction efficiencies.

In other words, the design requirements of the grating 21 may besummarized as follows:

(1) The diffraction efficiency of the minus first transmitted ordershould be greater than a particular value, for both TE and TMpolarizations. This requirement is analogous to an overall loss value orattenuation for a multiplexer and/or demultiplexer. An exemplary valuemay be about 98%, although other values such as 90%, 92%, 95%, 99% andso forth may be used.

(2) The diffraction efficiencies of TE and TM polarizations shoulddiffer from each other by less than a particular value. This isanalogous to a polarization dependent loss value for a multiplexerand/or demultiplexer, which arises from fluctuations in the incidentpolarization state. An exemplary value may be about 0.03 dB, 0.05 dB,0.10 dB, 0.15 dB and 0.25 dB, although other values may be used.

(3) The diffraction efficiencies should stay within their specificationsfor reasonable tolerances in usage (such as incident angle and/orwavelength), and reasonable tolerances in manufacturing processes (suchas thicknesses, duty cycles and/or wall angles). Collectively, thesetolerances or perturbations may be referred to as a “process window”,and it is desirable that the grating performance does not varysignificantly over the process window.

The gratings 11 and 21 of FIGS. 1-3 are generic in nature, and are drawnonly to show the orientations of the reflected and transmitteddiffracted orders, the angle of incidence, and the orientations of TEand TM polarizations. For more specific gratings, we refer to FIGS.4-14.

FIG. 4 shows a grating 41 having four layers and three differentmaterials, denoted as A, B and C. The grating materials A, B and C haverefractive indices n_(A), n_(B) and n_(C), respectively. The grating maybe disposed on a layer 45, which may be an etch stop useful during themanufacturing process or may be provided for other purposes, or may bedisposed directly on a substrate 44 that supports the grating. Multiplelayers such as 45 may be provided between the grating features and thesubstrate 44, if desired, without disturbing the adjacency of thegrating features and the substrate 44. The substrate may be flat orplanar on the side having the grating, but the body of the substrate mayhave any convenient shape.

An incident beam 42 strikes the grating, and the minus first diffractedorder in transmission forms the exiting beam 43. It should be noted thatthe incident and exiting beams are not drawn to scale; both are actuallymuch larger than the grating features themselves. The diffractionefficiencies of the minus first reflected order, the zeroth reflectedorder and the zeroth transmitted order are sufficiently low to as to beconsidered negligible; hence, they are not drawn in FIG. 4. Thediffraction efficiency of the minus first transmitted order may bemaximized for both TE and TM polarizations, and may be up to 98% orlarger.

The grating of FIG. 4 has four layers, with three different materialsand a distinct material for each layer. The refractive index profile forthe grating 41 is shown in a plot at the bottom of FIG. 4. For thisparticular example, as one moves longitudinally away from the substrate(i.e., along a surface normal) from material B, to material A, tomaterial B, to material C, the refractive index increases, thendecreases. There is a local maximum in the longitudinal refractive indexprofile at the layer for material A. This is merely an exemplaryrefractive index profile, and other suitable profiles may be used,including profiles that increase or decrease monotonically as one moveslongitudinally outward from the substrate.

Note that the functions of the materials A, B and C are all intertwinedin the grating 41. One cannot say, for example, that the layer made frommaterial C plays an exclusive role, such as an antireflection coating.Rather, it is the combination of the four layers, all taken together,that determines the characteristics of the grating 41.

Although the longitudinal extents (or, equivalently, heights or depths)of the four layers are drawn as equal in FIG. 4, they may all havedifferent heights. The heights may be varied, and may all vary from lessthan a micron to several microns each. The heights may be determined bysimulation, using any of several commercially available simulationpackages.

Exemplary materials for the substrate 44 may include synthetic fusedsilica, which has a refractive index of 1.444 at a wavelength of 1550nm, a borosilicate crown glass such as BK7 (n=1.501 at 1550 nm), or aflint glass such as SF2 (n=1.613 at 1550 nm) or SF11 (n=1.745 at 1550nm), or other optical glasses such as LaSFN9 (n=1.813 at 1550 nm), BaK1(n=1.555 at 1550 nm) or F2 (n=1.595 at 1550 nm). Other suitablesubstrate materials may also be used.

Exemplary grating materials may include silicon dioxide, SiO₂(n≈1.44-1.47 at 1550 nm, depending on the vendor and depositionprocess), titanium dioxide, TiO₂ (n≈2.20-2.36 at 1550 nm), or tantalumpentoxide, Ta₂O₅ (n≈2.00-2.11 at 1550 nm). Note that “tantalum” may alsobe known as “tantalium”, and “pentoxide” may also be known as“pentaoxide”. Note also that these materials are essentially transparentover the wavelength range of interest; there is essentially noabsorption over these wavelengths. Other suitable grating materials maybe used as well, including a variety of oxides, fluorides, nitrides,carbides and diamond.

As a specific example, material B may be Ta₂O₅, material A may be TiO₂,and material C may be SiO₂.

The etch stop layer may be any suitable material, such as Al₂O₃ or CaF₂.In general, the etch stop should be relatively resistant to the etchingagent. A suitable etching agent may be a fluorine plasma, although othersuitable etching agents may be used.

An exemplary manufacturing process for the grating is as follows. First,the optional etch stop 45 may be deposited on the substrate 44. Next,the grating materials A, B and C may be deposited sequentially onto theetch stop (or directly onto the substrate) in a manner analogous to thinfilm deposition. The grating materials may be deposited in essentiallycontinuous planes, without the grating structure. Next, aphotolithographic process may be used, in which the grating structuremay be etched into the A, B and C materials. If there is an etch stoppresent on the substrate, the etching may be continued until the etchstop is reached. Use of an etch stop may be preferred, in that the etchstop sets the etch depth and avoids etching into the substrate 44,rather than the relatively imprecise use of a known etch rate and atimer. This manufacturing process is merely an example, and othersuitable manufacturing processes may be used. If the etchingcharacteristics of the etch stop 45 and the substrate 44 aresufficiently different, the grating structure may be etched into theetch stop 45 if desired, without etching into the substrate 44.

A quantity commonly known as the “duty cycle” is the ratio of thegrating feature width (i.e., the lateral extent of the grating feature),divided by the grating period (i.e., the center-to-center lateralspacing of the grating features). The duty cycle of a grating may varyfrom 0% to 100% in principle; duty cycles between 20% and 80% are moretypical, with a preferable range of about 40% to about 70%. A commontarget duty cycle may be about 55%, although other target duty cyclesmay be used.

Note that the grating feature walls in FIG. 4 are essentiallyrectangular (i.e., parallel to the surface normal). Such rectangularwalls may be considered desirable, and may result from etching directly“downward” with little or no lateral effects. In practice, there may besome lateral etch effects that result in a slight incline to the walls.

Alternatively, there may be some desirable characteristics from adeliberately finite wall slope, although the etch process to make such aslope may be more difficult. A finite wall slope produces trapezoidalwalls. Note that the walls may be asymmetric or symmetric.

Note also that although the grating is shown in FIG. 4 as facing awayfrom the incident beam 42, the grating may also be located on theopposite side of the substrate 44, facing toward the incident beam. Thearrangement of FIG. 4 may be preferable, in that an antireflectioncoating on the planar side of the substrate need only be optimized forone incident angle, rather than a range of incident angles for thereverse arrangement. Such an antireflection coating may reduceFabry-Perot (etalon) effects within the substrate.

FIG. 5 shows a grating 51 that has six layers, using three materials A,B and C. The grating 51 as shown is disposed directly upon an optionaletch stop 55, or may be disposed directly upon the substrate 54 if theetch stop 55 is not needed. An incident beam 52 strikes the grating 51.The grating has high diffraction efficiencies into the minus firsttransmitted diffracted order in both TE and TM polarizations. As aresult, most of the power in the incident beam 52 is directed into theminus first transmitted diffracted order, which forms the exiting beam53.

The grating 51 may have nearly rectangular walls and a duty cycle ofroughly 40% to 70%, although other wall angles and duty cycles may beused. In addition, the depths (or, equivalently, “heights” or“thicknesses”) of the various layers may be optimized and may take onany value up to several microns or more. The layer depths may bepredetermined by an optimization or simulation step, performed prior tomanufacturing the grating. The layer depths may be equal or unequal toeach other.

As a specific example, material A may be titanium dioxide, material Bmay be tantalum pentoxide, and material C may be silicon dioxide. Thisis merely an example, and any suitable materials may be used.

Note also that the edges of each of the layers A, B and C of the gratingfeatures are mutually aligned. While this is desirable in practice,there may be some desirable characteristics from a deliberatemisalignment, although the process to achieve such a misalignment may bemore difficult.

The refractive index profile of the grating 51 is plotted at the bottomof FIG. 5. Note that the profile does not vary monotonically as in FIG.4, but has at least one local maximum and minimum. In this case, thereare two local maxima, located at the layers for material A. Likewise,there is one local minimum, located at the middle layer for material B,located in this case between the layers for material A. These localextrema in the refractive index profile need not be located exactly asdrawn in FIG. 5, but can have any suitable location in the grating 51.

For instance, the refractive index profiles shown in FIGS. 6 and 7 areanalogous to those shown in FIGS. 4 and 5, and correspond to a gratingwith four layers, formed from two materials. In the four layer gratingsrepresented by FIGS. 6 and 7, the refractive index profile goes throughtwo local extrema. In these refractive index profiles, there is onelocal maximum and one local minimum, located at the central two layers.

Two further examples of refractive index profiles with local extrema areshown in FIGS. 8 and 9. The gratings represented by FIGS. 8 and 9 bothhave four layers and use three different materials. Both also have onelocal maximum and one local minimum in their refractive index profiles,located at the central two layers.

It will be readily apparent to one of ordinary skill in the art thatthere may be additional local maxima and minima in the refractive indexprofile, for additional layers and/or additional materials used in thegrating.

It should also be noted that there may be local maxima and/or localminima in the refractive index profile even if a single material isused, if the material has a continuously varying refractive index, suchas a gradient index material. FIGS. 10-13 show examples of refractiveindex profiles that have one local extremum, for a material with arefractive index that varies between n_(L) and n_(H). It will be readilyunderstood by one of ordinary skill in the art that such a gradientindex material may be used in combination with other materials and otherlayers to form local extrema in the refractive index profile.

FIG. 14 shows a refractive index profile having two local extrema,denoted by refractive indices n₁ and n₂. This profile may correspond toa single layer that has a continuously varying refractive index profile.

It will be beneficial to summarize thus far. A grating is producedhaving a high diffraction efficiency into the minus first diffractedorder in transmission, for both TE and TM polarizations. The incidentangle may optionally be chosen so that the minus first diffracted orderin reflection would be retroreflected back to the incident beam. Thegrating may be formed from various materials and/or layers, where thethicknesses of the individual layers may be determined by anoptimization or simulation process.

In one aspect, the grating may have four or more layers, formed withthree or more materials, as in FIGS. 4 and 5.

In another aspect, the grating may have a longitudinal refractive indexprofile that contains at least two local extrema, such as a maximumand/or minimum. Such a grating may be formed from three or morematerials, as in FIGS. 5, 8 and 9, two materials, as in FIGS. 6 and 7,or a single material that has a continuously varying refractive index,as in FIGS. 10-14. Any or all of the materials may have a continuouslyvarying refractive index profile, as well.

In another aspect, the grating may include a material that has acontinuously varying refractive index profile.

Finally, it is beneficial to provide a specific numerical example of agrating of the form shown in FIG. 5. This exemplary grating has sixlayers and is formed from three materials, labeled as “A”, “B” and “C”in FIG. 5.

The design wavelength of the grating is 1550 nm, and plots are shown fora wavelength range of 1550 nm±75 nm. (This corresponds to a full-widthof 150 nm, or 9.7% of the center wavelength.)

The grating period (or pitch) is 1064 nm, or about 0.69 times the designwavelength. Equivalently, the period may be expressed as 940 lines permm. If the grating is to be used so that the minus first order isretroreflected back to the incident beam, the incident angle should besin⁻¹ (1550 nm/2/1064 nm), or about 47 degrees. A plot is shown for anincident angle range of 37 degrees to 57 degrees, corresponding to afull-width of 20 degrees.

The grating walls are roughly rectangular in profile. The duty cycle is55%, meaning that the grating features have a width of 55% of thegrating period, or about 585 nm.

The grating has six layers, as shown schematically in FIG. 5. Forconvenience, the layers are numbered 1 through 6, with 1 being adjacentto the substrate, and 6 being adjacent to air.

The substrate is fused silica, which has a refractive index of 1.444 atthe design wavelength of 1550 nm.

Layer 1 (corresponding to material B) is tantalum pentoxide, Ta₂O₅,which has a refractive index of about 2.0816±0.005 at 1550 nm. Thethickness (or, equivalently, height or depth) of layer 1 is 235 nm±5 nm.

Layer 2 (material A) is titanium dioxide, TiO₂, which has a refractiveindex of about 2.2815±0.005 at 1550 nm. The thickness of layer 2 is 190nm±5 nm.

Layer 3 (material B) is Ta₂O₅. The thickness of layer 3 is 170 nm±5 nm.

Layer 4 (material A) is TiO₂. The thickness of layer 4 is 190 nm±5 nm.

Layer 5 (material B) is Ta₂O₅. The thickness of layer 5 is 370 nm±10 nm.

Layer 6 (material C) is silicon dioxide, SiO₂, which has a refractiveindex of about 1.4490±0.005 at 1550 nm. The thickness of layer 6 is 320nm±10 nm.

Note that the six layer grating of this numerical example has alongitudinal refractive index profile similar to that shownschematically in FIG. 5, having two local maxima and one local minimum.It is understood that the layer thicknesses are as described numericallyabove, and are not all equal as shown schematically in FIG. 5.

The grating is oriented away from the incident beam, and it is assumedthat the side opposite the grating is perfectly anti-reflection coated.

FIG. 15 shows a plot of the calculated minus first order diffractionefficiencies for TE and TM polarizations, as a function of wavelength,for a constant incident angle of 47 degrees.

At the center wavelength of 1550 nm, the diffraction efficiencies of theminus first order in transmission for TE and TM polarizations are both99.4%. This corresponds to an insertion loss in dB of −10 log₁₀ (0.994),or less than 0.03 dB.

At the short wavelength edge of the range, at 1475 nm, the TEdiffraction efficiency is 98.6% (corresponding to an insertion loss ofabout 0.06 dB), and the TM diffraction efficiency is 96.3% (or 0.16 dBloss).

At the long wavelength edge of the range, at 1625 nm, the TE diffractionefficiency is 97.5% (or 0.11 dB loss), and the TM diffraction efficiencyis 96.1% (or 0.17 dB loss).

In addition to the insertion loss, an important quantity is thepolarization dependent loss (PDL) for the grating, found by taking thedifference in insertion loss (in dB) between the TE and TMpolarizations. The calculated polarization dependent loss is shown inFIG. 16, as a function of wavelength, for a constant incident angle of47 degrees.

At the center wavelength of 1550 nm, the polarization dependent loss isessentially 0 dB, because the diffraction efficiencies of the minusfirst order in transmission for TE and TM polarizations are essentiallyequal.

At the short wavelength edge of the range, at 1475 nm, the polarizationdependent loss is about (0.16 dB-0.06 dB), or about 0.10 dB. At the longwavelength edge of the range, at 1625 nm, the polarization dependentloss is about (0.17 dB-0.11 dB), or about 0.06 dB.

Although the PDL data in FIG. 16 may be calculated from the diffractionefficiency data in FIG. 15, it is beneficial to plot the PDL separatelybecause PDL is commonly listed as its own specification in manytelecommunications applications. Physically, the PDL represents thedifference between the minimum and maximum transmitted powers throughthe specified device, as the incident polarization is varied over allpolarization states. In general, it is highly desirable to minimize PDL,where possible, in addition to minimizing insertion loss.

To show that the grating is relatively insensitive to incident angle,FIG. 17 a plot of the calculated minus first order diffractionefficiencies for TE and TM polarizations, as a function of incidentangle, for a constant wavelength of 1550 nm.

At the center of the incident angle range (47 degrees), the diffractionefficiencies of the minus first order in transmission for TE and TMpolarizations are both 99.4%.

The diffraction efficiencies for both TE and TM polarizations are bothgreater than 99% over an incident angle range of about 44 degrees toabout 50 degrees.

The diffraction efficiencies for both TE and TM polarizations are bothgreater than 98% over an incident angle range of about 42 degrees toabout 52 degrees.

At an incident angle of 37 degrees, the TE diffraction efficiency is94.0%, and the TM diffraction efficiency is 94.9%.

At an incident angle of 57 degrees, the TE diffraction efficiency is95.8%, and the TM diffraction efficiency is 96.1%.

In general, if the diffraction efficiencies vary slowly with respect toincident angle, there may be a relaxed tolerance on the gratingorientation during the alignment and assembly process, leading to anincreased ease in manufacture of a device that uses the grating.

In addition, there may be configurations that explicitly use multipleincident angles within a particular range, such as a two-gratingconfiguration in which light dispersed from a first grating strikes asecond grating. An example of a two-grating configuration is disclosedin U.S. Pat. No. 6,978,062, titled “Wavelength division multiplexeddevice”, issued on Dec. 20, 2005 to Rose, et al., which is incorporatedby reference herein in its entirety.

Although the numerical examples provided herein are primarily for amultiplexer and/or demultiplexer for the telecommunications C-band(sometimes known as “conventional”), centered at a wavelength of 1550nm, other applications and wavelength regions may be used. For example,the S-band (or “short”), the L-band (or “long”) and the band centeredaround 1300 nm may all be used. In addition, the gratings describedherein may be used for laser pulse compression, and may operate atwavelength ranges centered around 800 nm or 1064 nm. Other applicationsand spectral regions may used as well.

The description of the invention and its applications as set forthherein is illustrative and is not intended to limit the scope of theinvention. Variations and modifications of the embodiments disclosedherein are possible, and practical alternatives to and equivalents ofthe various elements of the embodiments would be understood to those ofordinary skill in the art upon study of this patent document. These andother variations and modifications of the embodiments disclosed hereinmay be made without departing from the scope and spirit of theinvention.

1. An optical apparatus, comprising: an essentially transparentsubstrate; and a grating disposed adjacent the substrate and comprisingexactly four grating layers of at least three essentially transparentand respectively different materials; wherein the grating has a minusfirst order diffraction efficiency in transmission of greater than 90%for both TE and TM polarizations; and wherein: a first one of thegrating layers is tantalum pentoxide and is disposed adjacent thesubstrate; a second one of the grating layers is titanium dioxide and isdisposed directly upon the first grating layer; a third one of thegrating layers is tantalum pentoxide and is disposed directly upon thesecond grating layer; and a fourth one of the grating layers is silicondioxide and is disposed directly upon the third grating layer.
 2. Theoptical apparatus of claim 1, further comprising an etch stop layerdisposed between the first grating layer and the substrate, the etchstop layer being disposed directly upon the substrate, and the firstgrating layer being disposed directly upon the etch stop layer.
 3. Anoptical apparatus, comprising: an essentially transparent substrate; anda grating disposed adjacent the substrate and comprising exactly sixgrating layers of at least three essentially transparent andrespectively different materials; wherein the grating has a minus firstorder diffraction efficiency in transmission of greater than 90% forboth TE and TM polarizations; and wherein: a first one of the gratinglayers is tantalum pentoxide and is disposed adjacent the substrate; asecond one of the grating layers is titanium dioxide and is disposeddirectly upon the first grating layer; a third one of the grating layersis tantalum pentoxide and is disposed directly upon the second gratinglayer; a fourth one of the grating layers is titanium dioxide and isdisposed directly upon the third grating layer; a fifth one of thegrating layers is tantalum pentoxide and is disposed directly upon thefourth grating layer; and a sixth one of the grating layers is silicondioxide and is disposed directly upon the fifth grating layer.
 4. Theoptical apparatus of claim 3, further comprising an etch stop layerdisposed between the first grating layer and the substrate, the etchstop layer being disposed directly upon the substrate, and the firstgrating layer being disposed directly upon the etch stop layer.